43. f(x) = 2x³ - 3x² 12x + 1, [2, 3]
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
43
![**41–54** Find the absolute maximum and absolute minimum values of \( f \) on the given interval.
41. \( f(x) = 12 + 4x - x^2 \), \([0, 5]\)
42. \( f(x) = 5 + 54x - 2x^3 \), \([0, 4]\)
43. \( f(x) = 2x^3 - 3x^2 - 12x + 1 \), \([-2, 3]\)
44. \( f(x) = x^3 - 6x^2 + 9x + 2 \), \([-1, 4]\)
45. \( f(x) = x^4 - 2x^2 + 3 \), \([-2, 3]\)
46. \( f(x) = (x^2 - 1)^3 \), \([-1, 2]\)
47. \( f(t) = t\sqrt{4 - t^2} \), \([-1, 2]\)
48. \( f(x) = \frac{x^2 - 4}{x^2 + 4} \), \([-4, 4]\)
49. \( f(x) = xe^{-x^2/8} \), \([-1, 4]\)
50. \( f(x) = x - \ln x \), \(\left[\frac{1}{2}, 2\right]\)
51. \( f(x) = \ln(x^2 + x + 1) \), \([-1, 1]\)
52. \( f(x) = x - 2 \tan^{-1}x \), \([0, 4]\)
53. \( f(t) = 2 \cos t + \sin 2t \), \([0, \pi/2]\)
54. \( f(t) = t + \cot(t/2) \), \([\pi/4, 7\pi/4]\)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc87785b0-7b08-4187-be5d-f53b11d0a1a0%2F039fa99e-a006-4e5d-88bd-c8e20a67a0bb%2Fbzta55h_processed.png&w=3840&q=75)
Transcribed Image Text:**41–54** Find the absolute maximum and absolute minimum values of \( f \) on the given interval.
41. \( f(x) = 12 + 4x - x^2 \), \([0, 5]\)
42. \( f(x) = 5 + 54x - 2x^3 \), \([0, 4]\)
43. \( f(x) = 2x^3 - 3x^2 - 12x + 1 \), \([-2, 3]\)
44. \( f(x) = x^3 - 6x^2 + 9x + 2 \), \([-1, 4]\)
45. \( f(x) = x^4 - 2x^2 + 3 \), \([-2, 3]\)
46. \( f(x) = (x^2 - 1)^3 \), \([-1, 2]\)
47. \( f(t) = t\sqrt{4 - t^2} \), \([-1, 2]\)
48. \( f(x) = \frac{x^2 - 4}{x^2 + 4} \), \([-4, 4]\)
49. \( f(x) = xe^{-x^2/8} \), \([-1, 4]\)
50. \( f(x) = x - \ln x \), \(\left[\frac{1}{2}, 2\right]\)
51. \( f(x) = \ln(x^2 + x + 1) \), \([-1, 1]\)
52. \( f(x) = x - 2 \tan^{-1}x \), \([0, 4]\)
53. \( f(t) = 2 \cos t + \sin 2t \), \([0, \pi/2]\)
54. \( f(t) = t + \cot(t/2) \), \([\pi/4, 7\pi/4]\)
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